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Global well-posedness and decay estimates of strong solutions to the nonhomogeneous Boussinesq equations for magnetohydrodynamics convection
Proceedings of the Royal Society of Edinburgh Section A: Mathematics ( IF 1.3 ) Pub Date : 2020-09-15 , DOI: 10.1017/prm.2020.72 Xin Zhong
Proceedings of the Royal Society of Edinburgh Section A: Mathematics ( IF 1.3 ) Pub Date : 2020-09-15 , DOI: 10.1017/prm.2020.72 Xin Zhong
We deal with an initial boundary value problem of nonhomogeneous Boussinesq equations for magnetohydrodynamics convection in two-dimensional domains. We prove that there is a unique global strong solution. Moreover, we show that the temperature converges exponentially to zero in H 1 as time goes to infinity. In particular, the initial data can be arbitrarily large and vacuum is allowed. Our analysis relies on energy method and a lemma of Desjardins (Arch. Rational Mech. Anal. 137:135–158, 1997).
中文翻译:
磁流体动力学对流非齐次 Boussinesq 方程强解的全局适定性和衰减估计
我们处理二维域中磁流体动力学对流的非齐次 Boussinesq 方程的初始边值问题。我们证明了存在一个独特的全局强解。此外,我们证明了温度在H 1 随着时间的流逝。特别是,初始数据可以任意大,并且允许真空。我们的分析依赖于能量方法和 Desjardins 的引理(Arch. Rational Mech. Anal. 137:135–158, 1997)。
更新日期:2020-09-15
中文翻译:
磁流体动力学对流非齐次 Boussinesq 方程强解的全局适定性和衰减估计
我们处理二维域中磁流体动力学对流的非齐次 Boussinesq 方程的初始边值问题。我们证明了存在一个独特的全局强解。此外,我们证明了温度在